Basic and clinical research in the biomedical sciences demands improved instrumentation for accurate measurement and reliable analysis. The objective of this research is to improve the mass resolution of the time-of-flight mass spectrometer (TOF MS) such that it will be competitive with currently superior, but more expensive, high resolution mass spectrometers. In the proposed research the basic relations for a new ion focussing principle, termed velocity compaction (VC), will be derived for a deceleration first stage following a high voltage ion extraction section and in turn followed by an acceleration second stage with an expected resolution (M/DeltaMfwhm) in excess of 10,000. A series of computer simulations of the flight-times will be made, taking into account the effective ion plasma termperature. The result will be a series of simulated mass spectra from which mass resolution values can be predicted. Significant trends influencing the mass resolution will be plotted and analyzed, and a combination of practical dimensions will be chosen for a prototype model. Based on these results, design of a demonstration model, dual stage velocity compaction TOF MS will begin.